The centre of the circle `S=0` lie on the line `2x – 2y +9=0 & S=0` cuts orthogonally `x^2 + y^2=4`. Show that circle `S=0` passes through two fixed points & find their coordinates.

If centre of a circle lies on the line 2x - 6y + 9 =0 and it cuts the circle x^(2) + y^(2) = 2 orthogonally then the circle passes through two fixed points

Find the equation of the circle which cuts the circle x^(2)+y^(2)+5x+7y-4=0 orthogonally, has its centre on the line x=2 and passes through the point (4,-1).

Find the equation of the circle which cuts orthogonally the circle x^2 + y^2 – 6x + 4y -3 = 0 ,passes through (3,0) and touches the axis of y.

A variable circle which always touches the line x+y-2=0 at (1, 1) cuts the circle x^2+y^2+4x+5y-6=0 . Prove that all the common chords of intersection pass through a fixed point. Find that points.

The centre of the circle passing through the points (0,0), (1,0) and touching the circle x^2+y^2=9 is

The loucs of the centre of the circle which cuts orthogonally the circle x^(2)+y^(2)-20x+4=0 and which touches x=2 is

Center of a circle S passing through the intersection points of circles x^2+y^2-6x=0 &x^2+y^2-4y=0 lies on the line 2x-3y+12=0 then circle S passes through

The locus of the centre of the circle cutting the circles x^2+y^2–2x-6y+1=0, x^2 + y^2 - 4x - 10y + 5 = 0 orthogonally is

The equation of the circle which pass through the origin and cuts orthogonally each of the circles x^2+y^2-6x+8=0 and x^2+y^2-2x-2y=7 is

If the circle x^2 + y^2 + 2x - 2y + 4 = 0 cuts the circle x^2 + y^2 + 4x - 2fy +2 = 0 orthogonally, then f =